I'm trying to draw a five-pointed star; I have one pair of coordinates (I currently have that at the center of the star) and the "width" of the star.
Now, I've tried a lot around, but I can't figure out a way to find all 10 coordinates just based on these numbers.
I also need to rotate the star at angle x, so i need a way to change the coordinates.
(the thing is done through a custom library in python, but i just need a way to get these coordinates)
On
Prett much the same approach provided already, but I've included a diagram and gave the information in degrees rather than radians.
As you can see in the image, the coordinates are generated on an inner and outer circle. The radius of the smaller circle in the image is 2 units and the radius of the larger outer circle is 6 units. Each coordinate on the outer circle is $72^\circ$ around the circle from the previous coordinate. I started at $18^\circ$ so that a star point would be at $18^\circ+72^\circ=90^\circ$. The inner circle coordinates started at $54^\circ$ because it is the median angle of $18^\circ$ and $90^\circ$.
Every coordinate is written $(r~cos(\Theta),~r~sin(\Theta))$
For the tips you want to have 5 points evenly spread around a cycle with radius $r$, so take $$\{(r\cos(2\pi k/5+\pi/2),r\sin(2\pi k/5+\pi/2)) \mid k=0,...,4\}$$Do the same for the inner five points, but use a smaller radius and an additional $+2\pi/10$ within $\cos$ and $\sin$ to make them half way between the tips. (I have added $\pi/2$ to make the first tip point up, instead of right...)